mathematics hsc examinations by topichsc exam* questions by topic 2015 - 2019 licensed from nesa...

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au page 1

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

MATHEMATICS STANDARD 1 HSC Exam* Questions by Topic

2019 - 2015

Licensed

from NESA

Year 11 Course

Algebra

A1: Formulae and equations

A2: Linear relationships

Measurement

M1.1: Practicalities of measuring

M1.2: Perimeter, area and volume

M1.3: Units of energy and mass

M2: Working with time

Financial Mathematics

F1.1: Interest and depreciation

F1.2: Earning & managing money

F1.3: Budgeting and household expenses

Statistics Analysis

S1.1: Classifying and representing data

S1.2: Summary Statistics

S2: Relative frequency & probability

Year 12 Course

Algebra

A3.1: Simultaneous Linear Equations

A3.2: Graphs of practical situations

Measurement

M3: Right-angled triangles

M4: Rates

M5: Scale drawings

Financial Mathematics

F2: Investments

F3: Depreciation and loans

Statistical Analysis

S3.1: Statistical investigation process

S3.2: Exploring data from 2 variables

Networks and Paths

N2.1: Networks

N2.2: Shortest paths

Mathematics Standard 1 Reference Sheet (2020 HSC)

HSC Examination Papers Mathematics Standard 2

(2019) and Mathematics General 2 (including Maths General from 2015-2018); Mathematics and

Mathematics Extension 1 (2015-2019), and Mathematics Standard 1 (2019) © NSW Education

Standards Authority for and on behalf of the Crown in right of the state of New South Wales.

Questions by Topic from …

• 2019 Mathematics Standard 1 HSC

• NESA Mathematics Standard 1 Sample exam questions [SQ] (2019)

• Selected NESA Topic Guidance questions [TG] (2018)

• 2018 – 2015 Mathematics General 2 HSCs (eg 17 MG)

v2020



Year 11: Measurement

M2: Working with time

Syllabus: updated November 2019. Latest version @ https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-standard-2017

19 MS

1

2 What is the time difference between 8:35 am and 2:10 pm?

A. 5 hours and 25 minutes B. 5 hours and 35 minutes

C. 6 hours and 25 minutes D. 6 hours and 35 minutes

1

Solution

NESA 2019 Mathematics Standard 1 HSC Examination

SQ

MS

ME

5 Band

3-5

Part of a train timetable is shown.

Kris arrives at Amesham station at

1.45 pm and needs to get to Frampton as quickly as possible. Assuming all

trains run to schedule, what is the

EARLIEST timFe that Kris can arrive at

Frampton station? A. 2.29 pm

B. 2.38 pm

C. 2.47 pm

D. 2.55 pm

1

Solution

NESA Mathematics Standard 1 Sample examination materials

SQ

MS

ME

18 Band

3-5

Karin is in Athens, which is two hours ahead of Coordinated Universal Time (UTC).

Marco is in New York, which is five hours behind UTC.

(a) Karin is going to ring Marco at 10 pm on Tuesday, Athens time.

What day and time will it be in New York when she rings?

(b) Marco is going to fly from New York to Athens. His flight will leave on Wednesday at 9 am, New York time, and will take 11 hours.

What day and time will it be in Athens when he arrives?

1

2

Solution


Back

Reference

Sheet

[Yr 12 2020: not in

syllabus …. Projectmaths]

https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-standard-2017

http://www.projectmaths.com.au/assets/MS1-2019-2.pdf

http://www.projectmaths.com.au/assets/MS-SQ-ME5.pdf




18 MG

29a The time in Brisbane is 4

2

1 hours ahead of the time in New Delhi. John flew

from New Delhi to Brisbane via Singapore. His plane left New Delhi at 11:30 am

(New Delhi time), stopped for 3 hours in Singapore, and arrived in Brisbane at

9:00 am the following day (Brisbane time).

What was the plane’s total flying time?

3 Solution

NESA 2018 Mathematics General 2 HSC Examination

17 MG

27d Island A and island B are both on the equator. Island B is west of island A. The longitude of

island A is 5oE and the angle at the centre of the

earth (O), between A and B, is 30o.

(i) What is the longitude of island B? (ii) What time is it on island B when it is 10 am

on island A?

(iii) Projectmaths: not in Maths Stand 1

Not to scale

1

Solution


16 MG

27e Melbourne is located at (38oS, 145oE) and Dubai is located at (24oN, 55oE). (i) Calculate the difference in longitude between Melbourne and Dubai.

(ii) Show that the time difference between Melbourne and Dubai is 6 hours.

(iii) A plane leaves Melbourne on Friday at 11:30 pm. The flight time to Dubai is 15 hours.

What will be the time and the day in Dubai when the plane is due to land?

1

1

2

Solution


15 MG

14 Stockholm is located at 59oN 18oE and Darwin is located at 13oS 131oE. What is

the time difference between Stockholm and Darwin? (Ignore time zones and

daylight savings.) (A) 184 minutes (B) 288 minutes

(C) 452 minutes (D) 596 minutes

1 Solution


[Not in 2020 HSC, examined in 2021 HSC …. Projectmaths]



http://www.projectmaths.com.au/assets/GM-2018-29a.pdf

http://www.projectmaths.com.au/assets/GM-2017-27d.pdf


http://www.projectmaths.com.au/assets/GM-2016-27e.pdf

http://www.projectmaths.com.au/assets/GM-2015-14.pdf



Year 11: MS – F1: Statistical Analysis

S1.2: Summary statistics


19 MS

1

19 The heights, in centimetres, of 10 players on a basketball team are shown.

170, 180, 185, 188, 192, 193, 193, 194, 196, 202 Is the height of the shortest player on the team considered an outlier?

Justify your answer with calculations.

3 Solution


Back

Reference

Sheet





SQ MS

SA

2 Band

2-3

A dataset has the following five-number

summary.

If the range of the dataset is 7, what is the

minimum value of the dataset? A. 1 B. 2

C. 4 D. 5

1

Solution


SQ MS

SA

3 Band

2-3

A dataset has the following five-number

summary. What is the interquartile range of the dataset?

A. 1 B. 2

C. 3 D. 4

1

Solution


SQ MS

SA 10 Band

4-5

The box-plots show the results of a test sat by two classes,

A and B.

Which of the following statements

is true about Class B’s results when compared to

those of Class A?

1

Solution

A. The IQR for Class B’s results is larger than that for Class A’s results.

B. The results for Class B are more consistent than those of Class A. C. 25% of Class B’s results are higher than all of Class A’s results.

D. 25% of Class B’s results are lower than half of Class A’s results.


SQ

MS SA

11 Band

5-6

The dot plots show the class

scores in tests taken before

and after a unit of work was

completed.

They are drawn on the same

scale.

Which statement about the

change in scores is correct?

1

Solution

A. The mean increased and the standard deviation decreased. B. The mean increased and the standard deviation increased.

C. The mean decreased and the standard deviation decreased.

D. The mean decreased and the standard deviation increased.


SQ MS

SA

12 Band

5-6

In a computer game, a player scored 180, 183, 184, 186 and 192 in the first five

rounds. After playing a sixth round, the player’s average score increased by 1.

What was the player’s score in the sixth round? A. 185 B. 186 C. 191 D. 193

1

Solution


http://www.projectmaths.com.au/assets/MS-SQ-SA2.pdf







SQ MS

SA

17 Band

3-6

The diagram shows the distribution

of the ages of children in a town in

2008 and 2018.

In 2008 there were 1750 children aged 0 – 18 years.

(a) The number of children aged

12 – 18 years was the same in

both 2008 and 2018. How many children aged 0 – 18 years were

there in 2018?

2

Solution

(b) What would be ONE possible implication for government planning as a

consequence of the change in the distribution of ages from 2008 to 2018? Justify your answer with reference to the data provided.

2


SQ MS

SA

24 Band

3-4

Write down the five-number summary for the dataset 2, 4, 6, 9, 12, 18.


2

Solution

18 MG

1 A set of scores has the following five-number summary.

lower extreme = 2 lower quartile = 5 median = 6 upper quartile = 8 upper extreme = 9

What is the range?

A. 2 B. 3 C. 6 D. 7

1 Solution


18 MG

6 A set of data is displayed

in this dot plot.

Which of the following best describes this set of

data?

A. Symmetrical

B. Positively skewed C. Negatively skewed

D. Normally distributed

1

Solution


18 MG

11 A set of data is summarised in this

frequency distribution table.

Which of the following is true

about the data?

A. Mode = 7, median = 5.5 B. Mode = 7, median = 6

C. Mode = 9, median = 5.5

D. Mode = 9, median = 6

1 Solution









18 MG

26

d

The graph displays the mean

monthly rainfall in Sydney and

Perth.

(i) For how many months is the mean monthly rainfall

higher in Perth than

Sydney?

(ii) For which of the two cities is the standard deviation

of the mean monthly

rainfall smaller? Justify your

answer WITHOUT calculations.

1

1

Solution


18 MG

26

e

A cumulative frequency table for a data

set is shown.

What is the interquartile range for this

data set?

2 Solution


17 MG

1 The box-and-whisker plot for a set of data is shown.

What is the median of this set of data?

(A) 15 (B) 20 (C) 30 (D) 35

1 Solution


17 MG

27

a

Jamal surveyed eight households in his street. He asked them how many kilolitres

(kL) of water they used in the last year. Here are the results.

220, 105, 101, 450, 37, 338, 151, 205 (i) Calculate the mean of this set of data.

(ii) What is the population standard deviation of this set of data, correct to one

decimal place?

1

1

Solution


17 MG

30

a

A set of data has a lower quartile (QL) of 10 and an upper quartile (QU) of 16.

What is the maximum possible range for this set of data if there are no outliers?

2 Solution


16 MG

19 A soccer referee wrote down the number of goals scored in 9 different games during

the season. 2, 3, 3, 3, 5, 5, 8, 9,

The last number has been omitted. The range of the data is 10.

What is the five-number summary for this data set?

(A) 2, 3, 5, 8.5, 12 (B) 2, 3, 5, 8.5, 10 (C) 2, 3, 5, 8, 12 (D) 2, 3, 5, 8, 10

1 Solution



http://www.projectmaths.com.au/assets/GM-2018-26e.pdf







16 MG

21 A grouped data frequency

table is shown. What is the

mean for this set of data?

(A) 6.5 (B) 10.5

(C) 11.9

(D) 12.4

1 Solution


16 MG

22 The box-and-whisker plots show the results of a History test and

a Geography test.

In History, 112 students

completed the test.

The number of students who scored above 30 marks was the

same for the History test and

the Geography test.

How many students completed the Geography test?

(A) 8 (B) 50

(C) 56 (D) 112

1 Solution


16 MG

27

b

A small population consists of three students of heights 153 cm, 168 cm and

174 cm. Samples of varying sizes can be taken from this population. What is the mean of the mean heights of all the possible samples? Justify your answer.

2 Solution


16 MG

27c

The heights of 400

students

were

measured.

The results

are displayed

in this cumulative

frequency

polygon.

Use the

polygon to

estimate the

interquartile

range.

2

Solution




http://www.projectmaths.com.au/assets/GM-2016-27b.pdf

http://www.projectmaths.com.au/assets/GM-2016-27c.pdf



16 MG

29

c

The ages of members of a

dance class are shown in the back-to-back stem-and-leaf

plot. Pat claims that the women

who attend the dance class are

generally older than the men. Is Pat correct? Justify your answer

by referring to the median and

skewness of the two sets of

data.

3

Solution


15 MG

6 The times, in minutes, that a large group of students spend on exercise per day

are presented in the box-and-whisker plot.

What percentage of these students spend between 40 minutes and 60 minutes

per day on exercise?

(A) 17% (B) 20% (C) 25% (D) 50%

1 Solution


15 MG

27

d

In a small business, the seven employees earn the following wages per week:

$300, $490, $520, $590, $660, $680, $970.

(i) Is the wage of $970 an outlier for this set of data? Justify your answer with calculations.

(ii) Each employee receives a $20 pay increase. What effect will this have on

the standard deviation?

2

1

Solution


15 MG

29

d

Data from 200 recent house sales are

grouped into class intervals and a cumulative frequency histogram is

drawn.

(i) Use the graph to estimate the

median house price.

(ii) By completing the table,

calculate the mean house price.

1

3

Solution








Year 12: MS – M: Measurement

M4: Rates


19 MS

1

3 Sugar is sold in four different sized packets. Which is the best buy?

A. 100 g for $0.40 B. 500 g for $1.65 C. 1 kg for $3.50 D. 2 kg for $6.90

1

Solution


19 MS 1

5 Which expression can be used to convert a speed of 3 metres per minute to a

speed in centimetres per second?

A. 3 × 100 ÷ 60 B. 3 × 100 × 60 C. 3 ÷ 100 ÷ 60 D. 3 ÷ 100 × 60

1

Solution


Back

Reference

Sheet






19 MS

1

6 When blood pressure is measured, two numbers are recorded: systolic pressure

and diastolic pressure. If the measurements recorded are 130 systolic and 85 diastolic, then the blood pressure is written as ‘130 over 85’. The bars on the

graph indicate the healthy ranges of blood pressure for people of various ages.

1

Solution

Which person has both

blood pressure measurements in the

healthy range for their

age?

A. Stella aged 23 with blood pressure 120

over 72

B. Shane aged 35 with

blood pressure 124 over 90

C. Jon aged 54 with blood

pressure 137 over 94

D. Annie aged 61 with

blood pressure 142 over 88


19 MS

1

8 Heart rate is measured in beats per minute. Maximum heart rate (MHR) is calculated using the following formula.

MHR = 220 – age

Target heart rates are calculated as a percentage of MHR.

Felicity’s age is 28. Her trainer calculates that her target heart rate range is 60% to 80% of her MHR.

Which of the following lies within this target heart rate range?

A. 100 beats per minute B. 140 beats per minute

C. 180 beats per minute D. 220 beats per minute

1

Solution


19 MS1

29 Concrete is made by mixing cement,

sand and aggregate. Different types of concrete are

produced by changing the ratio of the

mix of these materials.

The table shows the ratio of the materials for different types of

2

Solution

concrete and examples of their common use.

The amount of concrete required for a patio slab is 3.5 cubic metres.

How many cubic metres of sand will be needed?


SQ MS Band

3-4

ME 6

A car travels 560 km on 60 L of petrol. What is its fuel consumption?

A. 7.3 L/100 km B. 8.7 L/100 km C. 9.3 L/100 km D. 10.7 L/100 km

1

Solution









SQ

MS Band

3-4

ME

12

The table shows the average

energy used, in kilojoules per kilogram of body mass, by a

person walking for 30 minutes

at different speeds. Sam, who

weighs 65 kg, drinks a

1

Solution

regular cappuccino made with full cream milk. It contains 73 kilocalories.

For approximately how long must Sam walk at 3 km/h to burn off the energy

contained in the cappuccino? (1 kilocalorie = 4.184 kJ.)

A. 20 minutes B. 25 minutes C. 90 minutes D. 120 minutes


SQ MS Band

4-5

ME 14

Blood pressure is measured using two numbers: systolic

pressure and diastolic pressure.

If the measurement shows 120

systolic and 80 diastolic, it is

written as ‘120 over 80’. The bars on the graph show the

normal ranges of blood pressure

for people of various ages.

Jamie, aged 42, had a blood pressure of 180 over 130. A

doctor prescribed Jamie a

medication to reduce his blood

pressure. To check that the medication was being effective,

the doctor measured Jamie’s

blood pressure for 10 weeks and

recorded the following results. Based on these results, from

1

Solution

which week was Jamie’s blood pressure consistently in the normal range?

A. Week 4 B. Week 5 C. Week 6 D. Week 7


SQ

MS Band

2-6

ME

16

The diagram shows the shape and

dimensions of an outdoor area which is to be

tiled. Tiles are sold in boxes. Each box holds one

square metre of tiles.

When calculating the number of tiles

required, 10% more tiles are needed due to cutting and wastage.

Delivery of tiles is charged at a base rate of

$55, plus a handling fee of $8 per box.

Find the total cost of delivering the boxes of tiles required for this area.

NOT TO SCALE

4 Solution










SQ

MS Band

3-6

ME

19

The diagram shows the three towns X, Y

and Z. Town Z is due east of Town X. The bearing of Town Y from Town X is N39oE

and the bearing of Town Z from Town Y is

S51oE.

The distance between Town X and Town Y is 1330 km.

A plane flies between the three towns.

(a) Mark the given information on the

diagram and explain whyXYZ is 90o.

2

Solution

(b) Find the distance between Town X and Town Z to the nearest kilometre.

(c) If the speed of the plane is 570 km/h, how long does the flight take from

Town X to Town Y, in hours and minutes?

2

2


SQ MS Band

4-5

ME20

Blood pressure is measured using two numbers: systolic pressure

and diastolic pressure. If the

measurement shows 120 systolic

and 80 diastolic, it is written as

‘120 over 80’. The bars on the graph show the

normal ranges of blood pressure

for people of various ages.

(a) What is the normal range of blood pressure for a 42-year-

old?

(b) Jamie, aged 42, had a blood

pressure of 180 over 130. A doctor prescribed Jamie a

medication to reduce his blood

pressure. To check that the

medication was being

effective, the doctor measured Jamie’s blood pressure for

1

3

Solution

10 weeks and recorded the following results.

With reference to the data provided, comment on the effectiveness of the

medication during the 10-week period in returning Jamie’s blood pressure to the normal range.


SQ

MS Band

3-5

ME

21

A student travels to and from university five days each week. She compares the

costs of two different modes of travel.

Her motorcycle uses one litre of fuel for every 17 km travelled. The cost of fuel is $1.47/L and the distance from her home to the university car park is 34 km.

The cost of travelling by bus is $4.71 per trip.

Which mode of travel is cheaper per week and by how much? Support your

answer with calculations.

3

Solution


TG 1 An old washing machine uses 130 L of water per load.

A new washing machine uses 50 L per load.

How much water is saved each year if two loads of washing are done each week

using the new machine?

Solution

NESA Mathematics Standard 2 Year 11 Topic Guide: Measurement

NOT TO

SCALE






http://www.projectmaths.com.au/assets/MS1-TGR-1.pdf



17 MG

2 A car is travelling at 95 km/h. How far will it travel in 2 hours and 30 minutes?

(A) 38 km (B) 41.3 km (C) 218.5 km (D) 237.5 km

1 Solution


16 MG

26c Peta’s car uses fuel at the rate of 5.9 L/100 km for country driving and 7.3 L/100 km for city driving. On a trip, she drives 170 km in the country and 25 km

in the city. Calculate the amount of fuel she used on this trip.

2 Solution






Year 12: MS – N: Networks

N2.2: Shortest paths


19 MS1

28 The network diagram shows the tracks

connecting 8 picnic sites in a nature park. The vertices A to H represents

the picnic sites. The weights on the

edges represent the distances along

the tracks between the picnic sites, in

kilometres. (a) Each picnic site needs to provide

2

Solution

drinking water. The main water source is at site A. By drawing a minimum

spanning tree in the space below, calculate the minimum length of water pipes

required to supply water to all the sites if the water pipes can only be laid along the tracks.

(b) One day the track between C and H is closed. State the vertices that identify

the shortest path from C to E that avoids the closed track.

1


SQ

MS

NW

2 Band

3-4

In a town, there are four petrol stations

W, X, Y and Z. The table shows the length, in metres, of roads connecting

these petrol stations.

A petrol tanker needs to visit each

station.

What is the shortest distance it can travel if it starts at Station W?

A. 840 m B. 1000 m

C. 1120 m D. 1270 m

1 Solution


SQ

MS

NW

3 Band

3-4

A weighted network

diagram is shown below.

What is the weight of

the minimum spanning tree?

A. 10

B. 11

C. 12

D. 14

1

Solution


Back

Reference

Sheet



http://www.projectmaths.com.au/assets/MS-SQ-NW2.pdf






SQ

MS

NW

4 Band

3-4

This diagram shows the

possible paths (in km) for

laying gas pipes between

various locations. Gas is to be supplied from one location.

Any one of the locations can

be the source of the supply.

What is the minimum length of the pipes required to

provide gas to all locations?

A. 32 km B. 34 km

C. 36 km D. 38 km

1

Solution


SQ MS

NW 7

Band

2-4

In a town, there are four petrol stations W, X, Y and Z. The table shows the length,

in metres, of roads connecting these petrol

stations.

(a) Construct a network diagram to

represent the information in the table. (b) A petrol tanker needs to visit each

station.

Calculate the shortest distance that can

2

2

Solution

be travelled by the petrol tanker. In your answer, include the order that the petrol stations are refilled.


SQ

MS

NW

8 Band

2-6

A park has five areas, A, B, C, D and E,

which are connected by pathways.

The table shows the length of some of the

pathways, in metres.

The following network diagram is drawn to

represent this information and a correct

minimum spanning tree is shown by the

4 Solution

solid lines.

Complete the network

diagram including a

possible value for each of

the two edges AE and BC,

and justify why AE and BC were not included as part

of the minimum spanning

tree.


NOT TO SCALE









TG 1 A computer network is to be built in a

school. The rooms and the cost of connecting the rooms are shown in the

diagram. Using a minimum spanning tree,

determine the smallest cost to connect all

the rooms.

Solution

NESA Mathematics Standard 2 Year 11 Topic Guide: Networks

TG 2 Draw the minimum spanning tree for this

network.

Solution


TG 3 Draw the minimum spanning tree for this

network.

Solution


TG 4 Identify the shortest distance from A to H.

Solution


TG 5 Identify the shortest distance from A to J.

Solution


http://www.projectmaths.com.au/assets/MS1-TGSP-1.pdf







TG 6 Determine the weight of the minimum

spanning tree for this network.

Solution


TG 7 Consider the following network.

(a) Determine the minimum spanning tree.

(b) Find the length of the shortest path

from A to E in the network.

Solution


TG 8 The following table shows the travelling times in minutes between towns which are

connected directly to each other.

Note: The dash in a box indicates that towns

are not connected directly to each other.

(a) Draw a network diagram showing the

information on this table.

(b) Find the shortest travelling time

between A and E.

Solution







Reference Sheet

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mathematics hsc examinations by topichsc exam* questions by topic 2015 - 2019 licensed from nesa...

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